Binary Bonbons (or 'How I Cracked the Christmas Cracker Code')

At a recent holiday lunch, a couple of people on our table received a "Mystery Calculator." David enjoyed himself discovering how this worked.

I was at a Christmas lunch about two weeks before the holiday. Everyone had what I have always known as "Crackers," but in Australia -- for some reason -- these are known as "Bonbons." The idea is that everyone finds a Bonbon as part of the place setting at the dining table. You start the festivities by pulling them in half -- accompanied by a loud crack courtesy of some minor pyrotechnics -- to disgorge a silly hat, a silly joke, sometimes a useless piece of trivia, and a usually-useless gift.

I received a miniature pack of cards in mine, which I gave to someone else who wanted it. Of more interest (at least to me) was the fact that a couple of people on our table each received a "Mystery Calculator." This turned out to be a set of six cards with numbers printed on them along with instructions on how to find a number picked by your friend.

A couple of the old dears on our table had a go but couldn't get it right. I looked at the instructions, which were simple enough, and proceeded to amaze everyone with my mysterious ability to divine the number they had picked (this was more due to my ability to read and follow instructions, gained from long years working with electronic equipment, than to any actual mysterious ability).

The cards that were in the puzzle are shown below. What you do is get a friend to pick one number from any card. You then ask him to give you all the cards bearing that number. You then (unbeknownst to him, while concentrating on the cards and trying to give the impression of having psychic abilities) add up the numbers in the top left-hand corner of all the "good" cards and -- hey, presto! -- you arrive at the number your friend picked.

Astute readers will observe, as I quickly did, that the numbers in the top left of the six cards are all powers of two, and the largest number on the cards is 63. As I am one of the 10 kinds of people in the world who talk binary, I thought "Ah Ha! You can represent any number between 1 and 63 with a 6-bit binary number, and there are six cards..." A little pondering revealed that any particular power of 2 will appear 32 times in the binary numbers between 1 and 63, and there are 32 numbers on each card, so each card has the numbers on it that have a "1" in the binary digit position corresponding to the first number on the card. I have illustrated this with this Excel sheet, which illustrates how the numbers on the cards were derived.

You could, if you are one of the 10 kinds of people in the world who don't talk binary, use the cards as a decimal-to-binary translator. But as one who does, I thought this was a very clever use of binary, and I also thought there may be some EE Times readers who would be similarly impressed. Maybe you will print the cards out and mystify your kids and in-laws with your amazing abilities. The main thing, of course, is to have a great New Year!

I also have used '"PCB Designer by Niche Software" for years in my classroom. I recently had to upgrade to windows 7 running 64 bit. Now my PCD Designer will not run!!!!! (is 32 bit software) Have you come across a fix for this? I really like to use the software for my young students because everything else out there is too complex. Can you contact me Thank you in advance.

No. I was eight or nine years old at the time and did not know binary math. I recall amazing all the relatives and being stubborn about not telling how it was done because magicians were not allowed to reveal their secrets.

@Zwede - as I said, for the uninitiated you could use it as a decimal to binary converter for numbers less than 64. Just write "32 16 8 4 2 1" and underneath those numbers, write a 1 if your number is on the corresponding card, and 0 if it is not. Bingo - Binary representation of your number!

@Antedeluvian - of course I don't mind! I am also looking forward to more of your articles. I have a very good book called Excel by Example by a guy called Aubrey Kagan (unfortunately now out of print) which has some very good Excel tricks in it. I learned a lot from that! :-)